Toshiki Mabuchi

(Author)

Test Configurations, Stabilities and Canonical Kähler Metrics: Complex Geometry by the Energy Method (2021)Paperback - 2021, 26 March 2021

Test Configurations, Stabilities and Canonical Kähler Metrics: Complex Geometry by the Energy Method (2021)
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Part of Series
Springerbriefs in Mathematics
Print Length
128 pages
Language
English
Publisher
Springer
Date Published
26 Mar 2021
ISBN-10
9811604991
ISBN-13
9789811604997

Description

The Yau-Tian-Donaldson conjecture for anti-canonical polarization was recently solved affirmatively by Chen-Donaldson-Sun and Tian. However, this conjecture is still open for general polarizations or more generally in extremal Kähler cases. In this book, the unsolved cases of the conjecture will be discussed.

It will be shown that the problem is closely related to the geometry of moduli spaces of test configurations for polarized algebraic manifolds.

Another important tool in our approach is the Chow norm introduced by Zhang. This is closely related to Ding's functional, and plays a crucial role in our differential geometric study of stability. By discussing the Chow norm from various points of view, we shall make a systematic study of the existence problem of extremal Kähler metrics.

Product Details

Author:
Toshiki Mabuchi
Book Edition:
2021
Book Format:
Paperback
Country of Origin:
NL
Date Published:
26 March 2021
Dimensions:
23.39 x 15.6 x 0.76 cm
ISBN-10:
9811604991
ISBN-13:
9789811604997
Language:
English
Location:
Singapore
Pages:
128
Publisher:
Weight:
204.12 gm

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